How to achieve this low poly lighting?
I've looked at the other works from Alex Pushilin and here is my attempt to reproduce it.

Setup is very simple. One Sun Lamp with warm color and small Size and RGB Background (this one is with Spherical Gradient). 

For materials I've used Principled Shader with Roughness - 1.0.

Most important thing here is to use Filimic Color management. I've used Look > High Contrast with a little correction from RGB Curves.

Also I've lower a bit Saturation in Compositing. 

Every probably will need a little bit different settings.